Page 100 -

pollutioneffect Ifsomefeatureofaproblem Post production system (PPS) A finite
has an indirect and nonobvious adverse impact grammar X over a finite set of symbols K which
on the accuracy that can be achieved by a dis- produces a set of constructs, C, from an initial
cretization scheme, a pollution effect can be construct c ∈ C, such that each construct in C
0
observed. A prominent example is the deteriora- can be obtained from one or more symbols in
tion of certain asymptotic rates of convergence of K by a finite derivation, where each step in the
finite element schemes for second-order elliptic derivation is a rule π ∈ X.
i
boundary value problems in the presence of reen- Comment: The constructs were strings repre-
trant corner. Another case is the loss of accuracy senting logical predicates, and the grammar the
suffered by standard finite element schemes for rules of logical derivation and proof, in Post’s
the Helmholtz equation − u − κu = f when κ original formulation (E.L. Post, “Finite combin-
atory processes. Formulation I”, J. Symbolic
becomes large.
Logic, 1, 103–105 (1936)). The class of Post-
generated construct sets is a member of the class
polymer A substance composed of macro- of recursively enumerable sets. The grammar
molecules. may be deterministic or nondeterministic, but its
execution is not stochastic. See universal Turing
machine and von Neumann machine.
polymerization The process of converting
a monomer or a mixture of monomers into a
postfix An operator written after its
polymer.
operands. Thus for two operands x and y and
operator f , the syntax is xyf .
polynomial A linear combination of non- Comment: Remember calculators with
negative, integer powers of a variable (or reverse Polish notation? In many instances this
unknown) x, is the most natural order of all; for example,
exponentiation. See also functor, infix, prefix,
n
p(x ) = a + a x + ··· + a x . and relation.
0 1 n
posynomial A positive sum of polynomials
population genetics One can study genetics a(i,j)
j
j
i c X x(j) , where c > 0. Each mono-
j
from either a molecular point of view (see double
mial is the product
helix)orfromapopulationpointofview. Popula-
tion genetics studies where the gene is located in X x(j) a(i,j) = x(1) a(i,1) ·x(2) a(i,2) ·...·x(n) a(i,n)
j
a chromosome, and how it is passed from gener-
ation to generation from the pedigree of heredi- and [a(i, j)] is called the exponent matrix.
This is the fundamental function in geometric
tary markers.
programming.
population model A system of mathemat- potential energy, E ,V,V Energy of position
E ,V
E
p p p
ical equations representing the proposed relation or orientation in a field of force.
between the population sizes and their growth
rates. The often used equations in textbooks, potential-energy profile A curve describ-
such as exponential growth, logistic equation, ing the variation of the potential energy of the
predator-prey, and competition are simplified system of atoms that make up the reactants and
population models. products of a reaction as a function of one geo-
metric coordinate, and corrresponding to the
“energetically easiest passage” from reactants to
porous medium equation Let U ⊂ R n
products (i.e., along the line produced by join-
open and u : U × R → R. The porous medium ing the paths of steepest descent from the transi-
equation for u is tion state to the reactants and to the products).
For an elementary reaction, the relevant geo-
γ
u − (u ) = 0. metric coordinate is the reaction coordinate.For
t

© 2003 by CRC Press LLC